Professor Chandrajit Bajaj

• Lecture Hours -- Mon, Wed- 2:00 - 3:15 pm. BUR 220 or Zoom
• Office hours – Mon, Wed 5:00 p.m. - 6:00 p.m. or by appointment ( Zoom  or POB 2.324)
• Contact: bajaj@cs.utexas.edu, bajaj@oden.utexas.edu

NOTE: Please do not send messages (questions or concerns) through canvas because I rarely don’t check email messages on Canvas. All questions related to class should be posted through Piazza or bring them to the office hour. Here is the link to register for Piazza: You can also join via the Piazza Tab on the canvas course page

Teaching Assistant

Yi Wang

• Office hours – Tue/Thu 1:00 p.m. - 2:00 p.m. POB 2.102 or Zoom
• Contact: panzer.wy@utexas.edu

Note: Please attempt to make reservations a day before for office hours to avoid conflicts. 

Course Motivation and Synopsis

 

This course is on foundational mathematical, statistical and computational optimization theory of data sciences. We shall also reveal how this data driven  and modern predictive machine learning theory is applied to stochastic dynamical systems,  optimal control and multi-player games. These latter topics are foundational to  the training of multiple neural networks (agents) both cooperatively and in adversarial scenarios helping optimize the learning of all the agents.

An initial listing of lecture topics  is given in the syllabus below. This is subject to modification, given the background and speed at which we cover ground.  Homework exercises shall be given almost  bi-weekly.  Assignment solutions that are turned in late shall suffer a  10% per day reduction in credit, and a 100% reduction once solutions are posted. There will be a mid-term exam in class. The content will be similar to the homework exercises. A list of  topics will also be assigned as take home final projects, to train the best of  machine learned  decision makers. The projects will involve ML programming, oral presentation, and a written report submitted at the end of the semester.

This project shall  be graded, and be in lieu of a final exam.

The course is aimed at senior undergraduates and junior graduate students. Those in the 5-year master's program students, especially in the CS, CSEM, ECE, STAT and MATH. are welcome. You’ll need algorithms, data structures, numerical methods and programming experience (e.g. Python ) as a CS senior, mathematics and statistics at the level of CS, Math, Stat, ECE, plus linear algebra, computational geometry, plus introductory functional analysis and combinatiorial and numerical optimization (CS, ECE, CSEM , Stat and Math. students).  

Course Material.

1. [B1] Chandrajit Bajaj (frequently updated)  A Mathematical Primer for Computational Data Sciences 
   
2. [BHK] Avrim Blum, John Hopcroft and Ravindran Kannan. Foundations of Data Science
3. [BV] Stephen Boyd and Lieven Vandenberghe Convex Optimization
4. [M] Kevin Murphy Machine Learning: A Probabilistic Perspective
5. [MU] Michael Mitzenmacher, Eli Upfal Probability and Computing (Randomized Algorithms and Probabilistic Analysis)
6. [SD] Shai Shalev-Shwartz, Shai Ben-David Understanding Machine Learning, From Theory to Algorithms
7. [SB] Richard Sutton, Andrew Barto Reinforcement Learning
8. [Basar] Tamer Basar  Lecture Notes on Non-Cooperative Game Theory.
9. Extra reference materials .

TENTATIVE  COURSE OUTLINE (in Flux). 

Date	Topic	Reading	Assignments
Wed 01-19-2022	1. Introduction to Data Science, Geometry of Data, High Dimensional Spaces,  Belief Spaces   [Lec1] Next Generation Statistical Machine Learning [notes]	[BHK] Ch 1,2
Mon 01-24-2022	2. Learning High-Dimensional Linear Regression Models  [Lec2] Geometry of Vector, Matrix, Functional Norms  and Approximations [notes];	[SD] Ch 9, Appendix C [BHK] Chap 12.2,12.3	[A1] out today due by 02-07-2022, 11:59pm
Wed 01-26-2022	3. Learning Theory and Model Selection [Lec3] Probability, Information and Probabilistic Inequalities [notes]	[MU] Ch 1-3 [B1] Appendix
Mon 01-31-2022	4. Stochastic Machine Learning |:  Cross, Conditional and Relative Entropy,  [Lec 4] Log-Sum-Exponential-Stability [notes]	[MU] Chap 4, 24.2 [BHK] Chap 12.4,12.6
Wed 02-02-2022	5. Sampling in High Dimensional  Spaces [Lec5] Concentration of Measure  [notes]	[SD] Chap 12
Mon 02-07-2022	6. Statistical Machine Learning using MonteCarlo and Quasi-MonteCarlo [ Lec6] Quasi-Monte-Carlo Methods, Integration Error H-K Inequality  [notes]		[A1] due tomorrow (Feb 8)
Wed 02-09-2022	7.  Learning Dynamics I  - Markov Chain Monte Carlo Sampling [Lec7] Random Walk  [notes]	[BHK] Chap 4 [MU] Ch 7, 10	[A1] solution   [A2] out yesterday due before 02-23-2022, 11:59pm
Mon 02-14-2022	8. Convex Optimization for Machine Learning [notes]	[SD] Chap 24 [BV] Chap 1-5
Wed 02-16-2022	9. Non-convex Optimization , Projected Gradient Descent [Notes]	[BHK] Chap 2.7 [SD] Chap 23,24
Mon 02-21-2022	10.  Statistical Machine Learning I : Separating Mixture of Gaussians  (a)  Sampling [notes]  (b) Expectation Maximization   [notes]	[M] Chap 11
Wed 02-23-2022	11. Statistical Machine Learning II: Bayesian Modeling [notes]	[M]  Ch 2, 5	[A2] due today by 11:59pm. Solution shall post tomorrow  [A3] out tomorrow. due before 03-07-2022, 11:59pm
Mon 02-28-2022	12. Statistical Machine Learning III: Bayesian Inference, Conjugate Priors, Multivariate Gaussians [notes]	[M]  Ch 4
Wed 03-02-2022	13.  Statistical Machine Learning IV: Gaussian Processes I [notes]	[M]  Ch 15
Mon 03-07-2022	14: Statistical Machine Learning V: Gaussian Processes II [notes]	[M]  Ch 15	[A3] due by 11:59pm today.  Solution  posts tomorrow AM
Wed 03-09-2022	MIDTERM in Class		[Midterm Solution] posts tonight [A4] out tonight due by 03-23-2022, 11:59pm
Mon-Fri 03-14-2022- 03-19-2022	Spring Break- March 14-19, 2022
Mon 03-21-2022	15.  Random Projections,Johnson-Lindenstrauss, Compressive Sensing [notes]   Spectral Methods in Dimension Reduction -KPCA [notes]	[BHK] Chap 5
Wed 03-23-2022	16.  Spectral Methods for Learning : KSVM [Notes], Fischer LDA, KDA [notes]	[M] Chap 14	[A4] due by 5pm 03-25-22. Solution posts Mar 25.  [A5] out Fri Mar 25 due by 04-08-2022, 5pm
Mon 03-28-2022	17.Spectral Methods in Dimension Reduction -KPCA [notes]   EigenFaces [notes]		Final PROJECT topics posts this week Part 1: First Report due before 04-25-2022, 9:59pm
Wed 03-30-2022	18.Robust Sparse Recovery; Alternating Minimization  [notes2] Connections to Variational AutoEncoders [notes]
Mon 04-04-2022	19. SVM via Stochastic Optimization [notes] Stochastic Gradient Descent-- Simulated Annealing, Fockker-Planck [notes]	Non-convex Projected Gradient Descent [notes-references]	[A5] due by tomorrow 04-08-22 5pm. Solution shall post 04-08 .
Wed 04-06-2022	20.  Energy Based Optimization Loss Functions II: SGD  Adagrad, RMSProp, Adam, ...] [notes]	See references cited in notes
Mon 04-11-2022	21. Learning Dynamics,  Lyapunov Stability  and connections to Training Deep Networks [notes]	See references cited in notes
Wed 04-13-2022	22. Learning Dynamics with NeuralODES:   : Adjoint Method for BackProp [notes] Robust learning of PDE's using Gaussian Processes [arxiv]	See references cited in notes and paper
Mon 04-18-2022	23.  Learning Stochastic Dynamics and Optimal Control:  Dynamics with Stability, LQR [notes]	See references cited in [notes]
Wed 04-20-2022	24. Learning Stochastic Dynamics and Optimal Control: LQR, iLQR, DDP [notes]	See references cited in [notes]
Mon 04-25-2022	25. Geometry of  Reinforcement Learning :   Markov Decision Processes [notes]	[SB]  See Chap 3	Part 1 of Project Due Final Project Report Due May 09, 2022
Wed 04-27-2022	26.  Geometry of Reinforcement Learning:   Guided On-Policy, Off-Policy Methods [notes1]  [notes2]	[SB] See Chap 9, 10, 11
Mon 05-02-2022	27. Geometry of Game Theoretic Learning I :  Actionable Learning [[notes] Nash Equilibrium  [notes]	[Basar] See Lectures 1, 2, 3
Mon 05-04-2022	28. Geometry of Game Theoretic Learning II: Stackelberg Equilibrium [notes]	[Basar] See Lectures 8, 9
	Presentations TBD		Final Project Report Due on May 09

 

Project FAQ

1. How long should the project report be?

Answer: See directions in the Class Project List.  For full points, please address each of the evaluation questions as succinctly as possible. Note the deadline for the report is May 09 midnight. You will get feedback on your presentations,  that should also be incorporated in your final report.

Assignments, Exam, Final Project

There will be six take-home bi-weekly assignments,  one in-class midterm exam and one take home final project (in lieu of a final exam).  The important deadline dates are:

• Midterm: Wednesday, March 09, 2pm - 3:30pm , BUR 2.220
  
• Final Project Written Report, Due: May 09, 11:59pm

 

Assignments

There will be six written take-home HW assignments and one take-home final project report. Please refer to the above schedule for assignments and final project report due time.

Course Requirements and Grading

Grades will be based on these factors:

• In-class attendance and participation (5%)
• HW assignments (60% and with potential to get extra credit) 

6 assignments. Some assignments may have extra questions for extra points you can earn. (They will be specified in the assignment sheet each time.)

• In-class midterm exam (15%) 
• First Presentation & Report (10%)
• Final Presentation & Report (15%)  

Students with Disabilities. Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities, 471-6259, http://www.utexas.edu/diversity/ddce/ssd . 

 

Accommodations for Religious Holidays. By UT Austin policy, you must notify the instructor of your pending absence at least fourteen days prior to the date of observance of a religious holiday. If you must miss a class or an examination in order to observe a religious holiday, you will be given an opportunity to complete the missed work within a reasonable time before or after the absence, provided proper notification is given.

 

Statement on Scholastic Dishonesty. Anyone who violates the rules for the HW assignments or who cheats in in-class tests or the final exam is in danger of receiving an F for the course. Additional penalties may be levied by the Computer Science department,  CSEM  and the University. See http://www.cs.utexas.edu/academics/conduct/